please help me

Question

A dietician works in a hospital and prepares meals under guidance of a physician. suppose       for a particular patient, a physician prescribes a meal to have 600 calories, 40 g of protein, and 240 mg of vitamin C. The dietician decides to prepare the meal using steak (each 3- oz serving contains 300 Cal, 20 g of protein, and no vitamin C), baked potatoes   (one baked potato contains 100 Cal, 5 g of  protein and 20 mg of vitamin C), and Brussels sprouts (one 156-gserving contains 50 Cal,5 g of protein, and 100 mg of vitamin C). How many servings of each food are required to satisfy the physician’s requirements?

Answer 1

Hello JP.

 

This is a problem with 3 equations and 3 unknowns (variables).  Let's set this up.

 

S = # 3oz servings of steak

P = # baked potatoes

B = #156 g servings of brussel sprouts.

 

We can express calories as

300S + 100P + 50B = 600

 

We can express protein as

20S + 5P + 5B = 40

 

And we can express Vitamin C as

20P + 100B = 240

Notice that steak does not have vitamin c

 

Let's work with the vitamin C equation first

20P + 100B = 240

P +5B = 12

P = 12-5B

 

Let's use this relationship and substitute it for P in the calorie and protein equations

 

300S + 100(12-5B) + 50B = 600

300S + 1200 - 500B + 50B = 600

300S - 450B = -600

Let's reduce this equation by dividing all terms by 150

2S - 3B = -4

 

Now let's do the same thing for the protein equation

 

20S + 5(12-5B) + 5B = 40

20S + 60 - 25B + 5B = 40

20S - 20B = -20

Let's reduce this equation by dividing all terms by 20

S - B = -1

 

Let's put these two equations together.

2S - 3B = -4

S - B = -1

 

Multiply the 2nd equation by -2

2S - 3B = -4

-2S + 2B = 2

 

Now add these two equations together.  The 2S's cancel and we have

-B = -2

B = 2

 

Since

S-B=-1

S-2=-1

S=1

 

Finally

since

P = 12-5B

P = 12-5(2)

P = 12-10

P=2

 

So we should have 1 serving of steak, 2 servings of baked potato and 2 servings of brussel sprouts.